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A New Lower Bound for Deterministic Truthful Scheduling

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Algorithmic Game Theory (SAGT 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12283))

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Abstract

We study the problem of truthfully scheduling m tasks to n selfish unrelated machines, under the objective of makespan minimization, as was introduced in the seminal work of Nisan and Ronen [NR99]. Closing the current gap of [2.618, n] on the approximation ratio of deterministic truthful mechanisms is a notorious open problem in the field of algorithmic mechanism design. We provide the first such improvement in more than a decade, since the lower bounds of 2.414 (for \(n=3\)) and 2.618 (for \(n\rightarrow \infty \)) by Christodoulou et al. [CKV07] and Koutsoupias and Vidali [KV07], respectively. More specifically, we show that the currently best lower bound of 2.618 can be achieved even for just \(n=4\) machines; for \(n=5\) we already get the first improvement, namely 2.711; and allowing the number of machines to grow arbitrarily large we can get a lower bound of 2.755.

Supported by the Alexander von Humboldt Foundation with funds from the German Federal Ministry of Education and Research (BMBF). Yiannis Giannakopoulos is an associated researcher with the Research Training Group GRK 2201 “Advanced Optimization in a Networked Economy”, funded by the German Research Foundation (DFG). A full version of this paper is available at https://arxiv.org/abs/2005.10054.

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Authors and Affiliations

  1. TU Munich, Munich, Germany

    Yiannis Giannakopoulos, Alexander Hammerl & Diogo Poças

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  1. Yiannis Giannakopoulos
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  2. Alexander Hammerl
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  3. Diogo Poças
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Correspondence to Diogo Poças .

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  1. Institute of Mathematics, Augsburg University, Augsburg, Germany

    Tobias Harks

  2. Institute of Mathematics, Technical University Berlin, Berlin, Germany

    Max Klimm

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Giannakopoulos, Y., Hammerl, A., Poças, D. (2020). A New Lower Bound for Deterministic Truthful Scheduling. In: Harks, T., Klimm, M. (eds) Algorithmic Game Theory. SAGT 2020. Lecture Notes in Computer Science(), vol 12283. Springer, Cham. https://doi.org/10.1007/978-3-030-57980-7_15

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  • DOI: https://doi.org/10.1007/978-3-030-57980-7_15

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